Apparatus and method for transmitting/receiving signal in communication system

ABSTRACT

Disclosed is an apparatus and a method for transmitting/receiving a signal in a communication system, which generates an Affine Permutation Matrix-Low Density Parity Check (APM-LDPC) codeword by encoding an information vector in an APM-LDPC encoding scheme which is a preset structured LDPC encoding scheme, and detects the information vector by decoding the signal in a decoding scheme corresponding to the APM-LDPC encoding scheme, thereby making it possible to generate a Low Density Parity Check (LDPC) code in the form of maximizing a girth while minimizing complexity.

PRIORITY

This application claims priority to an application filed in the KoreanIndustrial Property Office on Jan. 13, 2006 and assigned Serial No.2006-004146, the contents of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an apparatus and a method fortransmitting/receiving a signal in a communication system, and moreparticularly to an apparatus and a method for transmitting/receiving asignal by using an Affine Permutation Matrix (APM)-Low Density ParityCheck (LDPC) code, which is an improved structured LDPC code, in acommunication system.

2. Description of the Related Art

Next-generation communication systems have evolved into the form of apacket service communication system for transmitting burst packet datato a plurality of Mobile Stations (MS), and the packet servicecommunication system has been designed to be suitable for mass datatransmission. Further, next-generation communication systems areactively considering using an LDPC code, together with a turbo code. TheLDPC code is known to have an excellent performance gain at high-speeddata transmission, and has an advantage in that it can enhance datatransmission reliability by effectively correcting errors due to noiseoccurring in a transmission channel.

Reference will now be made to FIG. 1, which illustrates the structure ofa signal transmission apparatus in a conventional communication systemusing an LDPC code.

Referring to FIG. 1, the signal transmission apparatus includes anencoder 111, a modulator 113 and a transmitter 115. First, if aninformation vector s to be transmitted occurs in the signal transmissionapparatus, the information vector s is delivered to the encoder 111. Theencoder 111 generates a codeword vector c, that is, a non-binary LDPCcodeword, by encoding the information vector s in a predeterminedencoding scheme, and then outputs the generated codeword vector c to themodulator 113. Here, the predetermined encoding scheme corresponds to anon-binary LDPC encoding scheme. The modulator 113 generates amodulation vector m by modulating the codeword vector c in apredetermined modulation scheme, and then outputs the generatedmodulation vector m to the transmitter 115. The transmitter 115 inputstherein the modulation vector m output from the modulator 113, executestransmission signal processing for the input modulation vector m, andthen transmits the processed modulation vector m to a signal receptionapparatus through an antenna.

Next, reference will be made to FIG. 2, which illustrates the structureof a signal reception apparatus in a conventional communication systemusing an LDPC code.

Referring to FIG. 2, the signal reception apparatus includes a receiver211, a demodulator 213 and a decoder 215. First, a signal transmitted bya signal transmission apparatus, such as shown in FIG. 1, is receivedthrough an antenna of the signal reception apparatus, and the receivedsignal is delivered to the receiver 211. The receiver 211 executesreception signal processing for the received signal to thereby generatea reception vector r, and then outputs the processed and generatedreception vector r to the demodulator 213. The demodulator 213 inputstherein the reception vector r output from the receiver 211, generates ademodulation vector x by demodulating the input reception vector r in ademodulation scheme corresponding to a modulation scheme applied to amodulator of the signal transmission apparatus (that is, the modulator113), and then outputs the generated demodulation vector x to thedecoder 215. The decoder 215 inputs therein the demodulation vector xoutput from the demodulator 213, decodes the input demodulation vector xin a decoding scheme corresponding to an encoding scheme applied to anencoder of the signal transmission apparatus (that is, the encoder 111),and then outputs the decoded demodulation vector x into a finallyrestored information vector ŝ.

Meanwhile, the LDPC code has performance approximating a channelcapacity limit presented in Shannon's channel coding theorem. In orderto generate an LDPC code having such good performance, a cycle and adensity distribution on the Tanner graph of an LDPC code must beconsidered, and particularly consideration must be given to maximizing agirth on the Tanner graph. Here, “girth” denotes a minimum cycle lengthon the Tanner graph of a parity check matrix of the LDPC code. Thereason why consideration must be given to maximizing the girth on theTanner graph is that a cycle on the Tanner graph must be generallylonger in order not to cause performance deterioration, such as an errorfloor, which occurs when there are many comparatively short-lengthcycles (for example, cycles having a length of 4), on the Tanner graph.

Thus, research is being conducted to provide schemes for generating aparity check matrix in such a manner so as not to produce short-lengthcycles on the Tanner graph, two typical ones of which are Scheme 1, inwhich short-length cycles are removed from a given random LDPC code, andScheme 2, in which an LDPC code with no short-length cycle isalgebraically generated. Scheme 2 is mainly used from these two schemesbecause the memory capacity required for storing parity check matrixesis large, and it is difficult to implement efficient LDPC encoding inthe case of Scheme 1. Here, an LDPC code generated by applying Scheme 2is called a structured LDPC code, and reference will now be made to aparity check matrix of a general structured LDPC code, with reference toFIG. 3.

As illustrated in FIG. 3, the parity check matrix of a generalstructured LPDC code has a structure in which the overall parity checkmatrix is divided into a plurality of blocks, and a permutation matrixcorresponds to each block. Here, it is assumed that the permutationmatrix has a size of L×L. As seen from FIG. 3, the parity check matrixof the structured LDPC code is divided into (p×q) number of blocks, anda permutation matrix corresponds to each block. In FIG. 3, P^(a) ^(pq)indicates a permutation matrix located at an intersection point of a pthblock row and a qth block column among the plurality of blocks. Here,the superscript “a_(pq)” is 0≦a_(pq)≦1 or a_(pq)=∞.

Further, the permutation matrix corresponding to each block is referredto as a “block matrix”. In the case where the respective block matrixeswithin the parity check matrix are selected to only an identity matrix,if the location of a non-zero element in the first row of each blockmatrix is determined, then the locations of the remaining non-zeroelements, that is, (L−1) number of elements, are determined. Thus, thememory capacity required for storing information on the overall paritycheck matrix is reduced to 1/L, as compared with that in the case wherethe locations of non-zero elements irregularly distributed in each blockmatrix are selected, that is, in the case where an LDPC code isgenerated by applying Scheme 1.

It can be noted from the foregoing that the structured LDPC code hasimproved performance by considering not only the memory capacityrequired for storing parity check matrix information, but also efficientencoding. However, the structured LDPC code which is currently proposedin the art has a drawback in that its cycle is affected by a parentmatrix thereof, and an upper limit is restricted by several numeralsrelated to its parent matrix irrespective of which code length andpermutation matrixes are selected.

SUMMARY OF THE INVENTION

Accordingly, the present invention has been made to solve at least theabove-mentioned problems occurring in the prior art, and an object ofthe present invention is to provide an apparatus and a method fortransmitting/receiving a signal in a communication system.

A further object of the present invention is to provide an apparatus anda method for transmitting/receiving a signal using a structured LDPCcode in a communication system.

A further object of the present invention is to provide an apparatus anda method for transmitting/receiving a signal using an APM-LDPC code,which is an improved structured LDPC code, in a communication system.

In order to accomplish these objects, the present invention generates anAPM-LDPC codeword by encoding an information vector in an APM-LDPCencoding scheme, which is a preset structured LDPC encoding scheme,thereby making it possible to generate an LDPC code in the form ofmaximizing a girth while minimizing complexity.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects, features and advantages of the presentinvention will be more apparent from the following detailed descriptiontaken in conjunction with the accompanying drawings, in which:

FIG. 1 is a block diagram illustrating the structure of a signaltransmission apparatus in a conventional communication system using anLDPC code;

FIG. 2 is a block diagram illustrating the structure of a signalreception apparatus in a conventional communication system using an LDPCcode;

FIG. 3 is a view illustrating a parity check matrix of a generalstructured LDPC code;

FIG. 4 is a view illustrating connected block cycles on the Tanner graphin accordance with the present invention; and

FIG. 5 is a view illustrating function chains of two different blockcycles connected with each other by p number of blocks on the Tannergraph in accordance with the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Hereinafter, preferred embodiments of the present invention will bedescribed with reference to the accompanying drawings. It should benoted that the similar components are designated by similar referencenumerals although they are illustrated in different drawings. Also, inthe following description, a detailed description of known functions andconfigurations incorporated herein will be omitted when it may obscurethe subject matter of the present invention. Further, it should be notedthat only parts essential for understanding the operations according tothe present invention will be described and a description of parts otherthan the essential parts will be omitted in order not to obscure thepresent invention.

The present invention provides an apparatus and a method fortransmitting/receiving a signal in a communication system. Further, thepresent invention provides an apparatus and a method fortransmitting/receiving a signal using an Affine Permutation Matrix(“APM”)-Low Density Parity Check (“LDPC”) code, which is an improvedstructured LDPC code, in a communication system. Further, althoughseparately described and illustrated herein, it is clear that aprocedure of transmitting a signal using the APM-LDPC code of thepresent invention may be applied to a signal transmission apparatus of acommunication system, which has a structure as illustrated in FIG. 1,and a procedure of receiving a signal by using the APM-LDPC code of thepresent invention may be applied to a signal reception apparatus of acommunication system, which has a structure as illustrated in FIG. 2.

First, assume that Z_(L)={0, 1, . . . , L−1} is an integer ring ofmodulo L, and Z*_(L)={iεZ_(L)|gcd(i,L)=1}. Further, for aεZ*_(L) andbεZ_(L), an Affine function ƒ_((a,b)) on Z_(L), which is defined byƒ_((a,b))(x)=ax+b, can be considered. The Affine function ƒ_((a,b)) canalso be extended to an L×L permutation matrix P^(ƒ) ^((a,b)) whose (i,j)th element is defined as the following Equation (1):

$\begin{matrix}{\lbrack P^{f_{({a,b})}} \rbrack = \{ \begin{matrix}1 & {{{if}\mspace{14mu} j} = {f_{({a,b})}(i)}} \\0 & {otherwise}\end{matrix} } & (1)\end{matrix}$

Hereinafter, for the convenience of explanation, the permutation matrixP^(ƒ) ^((a,b)) is referred to as an “Affine permutation matrix”, and anL×L zero matrix, a set of Affine functions on Z_(L) and a set of L×LAffine permutation matrixes, including the L×L zero matrix, will bedesignated by P^(∞), A_(L) and P_(L), respectively.

Consider an LDPC code C whose length is nL and which has a parity checkmatrix H as given in the following Equation (2):

$\begin{matrix}{H = \begin{bmatrix}P^{f_{11}} & p^{f_{12}} & \cdots & P^{f_{1n}} \\P^{f_{21}} & P^{f_{22}} & \cdots & P^{f_{2n}} \\\vdots & \vdots & \cdots & \vdots \\P^{f_{m\; 1}} & P^{f_{m\; 2}} & \cdots & P^{f_{mn}}\end{bmatrix}} & (2)\end{matrix}$

In Equation (2), ƒ_(ij) has a value of an Affine function related to(a_(ij),b_(ij))εZ*_(L)×Z_(L) for i and j or a value of ∞.

A structured LDPC code generated by applying the parity check matrix Hincluding Affine permutation matrixes is referred to as an “APM-LDPCcode”. Here, if the exponent a_(ij) of the Affine permutation matrix isequal to 1, p^(ƒ) ^(ij) denotes a circulant permutation matrix. Further,an APM-LDPC code satisfying a_(ij)=1 for all i and j is called aQuasi-Cyclic (QC) LDPC code. Further, for a fixed (a_(j), b_(j)), thelocations of all non-zero elements P^(ƒ) ^(ij) , for example, thelocations of elements having a value of 1, are uniquely determined.Thus, the memory capacity required for storing the parity check matrixof the APM-LDPC code is reduced to 1/L, as compared with that of arandomly-configured LDPC code.

For the purpose of this discussion, several terms are defined below:

(1) Parent Matrix

An m×n binary matrix M(H) can be generated by substituting zero matrixesand Affine permutation matrixes, included in a parity check matrix asexpressed by Equation (2), with 0 and 1, respectively, and the matrixgenerated in this way is referred to as a “parent matrix”.

(2) Function Matrix

A function matrix F(H) of the above-mentioned parity check matrix H maybe defined by the following Equation (3):

$\begin{matrix}{{F(H)} = \begin{bmatrix}f_{11} & f_{12} & \cdots & f_{1n} \\f_{21} & f_{22} & \cdots & f_{2n} \\\vdots & \vdots & \cdots & \vdots \\f_{m\; 1} & f_{m\; 2} & \cdots & f_{mn}\end{bmatrix}} & (3)\end{matrix}$(3) Function Extension

The parity check matrix H is generated by extending an m×n functionmatrix to an m×n matrix defined on P_(L), and such an extensionprocedure, expressed by H=E_(L)(F), is referred to as a “functionextension” procedure.

(4) Block Cycle and Overlap

If a cycle with a length of 2l exists on the Tanner graph of the parentmatrix M(H), then such a cycle is referred to as a “2l-sized blockcycle”. Further, if one Affine permutation matrix belongs to two or moreblock cycles, then this is referred to as an “overlap between blockcycles”.

(5) Function Chain

If a 2l-sized block cycle corresponding to 2l number of Affinepermutation matrixes P^(ƒ) ¹ , P^(ƒ) ² , . . . , P^(ƒ) ^(2l) exists inthe parity check matrix H within the parent matrix M(H), then (ƒ₁, . . ., ƒ_(2l)) is referred to as a function chain. Further, for 1≦i≦2l, P^(ƒ)^(i) and P^(ƒ) ^(i+1) are located in the same row or column block of theparity check matrix H, and P^(ƒ) ^(i) and P^(ƒ) ^(i+2) are located indifferent row and column blocks of the parity check matrix H. Here,P^(ƒ) ^(2l+1) =P^(ƒ) ¹ , and P^(ƒ) ^(2l+2) =P^(ƒ) ² .

(6) Connected Block Cycle

Reference will now be made to FIG. 4, which illustrates connected blockcycles on the Tanner graph according to the present invention.

As illustrated in FIG. 4, when two different block cycles are connectedwith each other by p number of edges, which are connected one afteranother, on the Tanner graph of an m×n binary matrix M(H), it can besaid that they are connected with each other by p number of blockscorresponding to the connected edges. In particular, if p=0, the blockcycles share one bit or check node within the m×n binary matrix M(H),which is referred to as “directly connected”.

(7) Composition of Functions

Given ƒ_(j), 1≦i≦s, a composition sequence can be defined by thefollowing Equation (4):

$\begin{matrix}{{\underset{i = 1}{\overset{s}{\odot}}{f_{i}(x)}}\overset{\bigtriangleup}{=}{f_{s} \cdot f_{s - 1} \cdot \ldots \cdot {f_{1}(x)}}} & (4)\end{matrix}$

In Equation (4), “∘” is a symbol indicating composition of functions.Here, ƒ∘g(x)=ƒ(g(x)). If ƒ_(i)=ƒ for all i, then this is abbreviated toƒ^(s)(x), and ƒ¹(x) is an inverse function of ƒ(x). For the convenienceof explanation, an operation as given in the following Equation (5) isnow defined:

$\begin{matrix}{{\underset{i = j}{\overset{s}{\otimes}}{f_{i}(x)}}\overset{\bigtriangleup}{=}{{f_{s}^{{({- 1})}^{s - i + 1}} \cdot \ldots \cdot f_{j + 2}^{- 1} \cdot f_{j + 1}}\ldots\mspace{11mu} f}} & (5)\end{matrix}$(8) Characteristic Function of Function Chain

For a given function chain (ƒ₁, . . . ,ƒ_(2l)), its characteristicfunction z(x) is defined as

${\overset{2l}{\underset{i = 1}{\otimes}}{f_{i}(x)}},$and if all ƒ_(i)(x) are Affine functions, then the characteristicfunction z(x) is also an Affine function.

Next, reference will be made to cycle properties of the APM-LDPC code.

Owing to the inherent structure of the APM-LDPC code's parity checkmatrix, the cycle properties of the APM-LDPC code can be algebraicallyanalyzed with ease. Now, an upper limit for a girth of the APM-LDPC codewill be detected, and the detected upper limit will be described incomparison with the upper limit of a QC-LDPC code. Here, the girthindicates a minimum cycle length on the Tanner graph of a parity checkmatrix.

First, Theorem 1, as will be described below, presents the necessary andsufficient condition under which the APM-LDPC code has a cycle.

Theorem 1

It is assumed that (ƒ₁, . . . , ƒ_(2l)) is a function chain whichcorresponds to a 2l-sized block cycle of an APM-LDPC code, and has aparity check matrix H and a characteristic function z(x). Further, let rbe a minimum positive integer satisfying the following Equation (6):z ^(r)(x ₀)≡x ₀ mod L  (6)

In Equation (6), x₀εZ_(L), and thus the block cycle corresponds to acycle which has a length of 2lr on the Tanner graph of the APM-LDPCcode.

Further, when z(x)=ax+b for (a,b)εZ*_(L)×Z_(L),z^(r)(x)=a^(r)x+(a^(r−1)+ . . . +a+1)b. Thus, a solution x₀ satisfyingz^(r)(x₀)=x₀ exists, which is identical togcd(a^(r)−1,L)|(a^(r−1)+a^(r−2)+ . . . +a+1)b. When a=1, Equation (6) isunder the same condition as rb≡0 mod L. Further, since the QC-LDPC codeis an LDPC code having an Affine function in the form ofƒ_(ij)(x)=x+b_(ij), Theorem 2 can be defined as follows:

Theorem 2

It is assumed that (ƒ₁, . . . , ƒ_(2l)) is a function chain whichcorresponds to a 2l-sized block cycles of an QC-LDPC code and hasƒ_(i)(x)=x+b_(i), and that r is a minimum positive integer satisfyingthe following Equation (7):

$\begin{matrix}{{r{\sum\limits_{i = 1}^{2l}{( {- 1} )^{i}b_{i}}}} \equiv {0{mod}\; L}} & (7)\end{matrix}$

Thus, the block cycle is a cycle which has a length of 2lr on the Tannergraph of the QC-LDPC code.

Using Theorems 1 and 2, cycles of the APM-LDPC code and the QC-LDPC codecan be expressed by a simple equation, which makes it possible to removeshort-length cycles on the Tanner graph. This will be described below.

First of all, it is assumed that matrixes, as given in the followingEquation (8), exist:

$\begin{matrix}{{F_{1} = \begin{bmatrix}{{2x} + 1} & {3x} \\{5x} & {4x}\end{bmatrix}},{F_{2} = \begin{bmatrix}{{2x} + 3} & {{3x} + 1} \\{{4x} + 5} & {x + 1}\end{bmatrix}},{F_{3} = \begin{bmatrix}x & {3x} \\{{5x} + 1} & {3x}\end{bmatrix}}} & (8)\end{matrix}$

In Equation (8), F₁ and F₂ are defined in A₇, and F₃ is defined in A₈.Further, for the matrixes, each function chain corresponding to a4-sized block cycle can be expressed by the following Equation (9):F₁:(2x+1,3x,4x,5x), F₂:(2x+3,3x+1,x+1,4x+5), F₃: (x,3x,3x,5x+1)  (9)

Thus, each characteristic function corresponding to each of the functionchains can be expressed by the following Equation (10):z ₁(x)=x+6,z ₂(x)=6x+1,z ₃(x)=5x+1  (10)

In the case of z₁(x) in Equation (10), the minimum positive integersatisfying Equation (6) is r=7, which indicates a cycle having a size of4×7=28 on the Tanner graph H₁=E₇(F₁). Further, in the case of z₂(x) inEquation (10), the minimum positive integer satisfying Equation (6) forx=4 is r=1, and for the remaining x, the minimum positive integersatisfying Equation (6) is r=2, which indicates that one cycle with asize of 4 and three cycles with a size of 8 exist on the Tanner graphH₂=E₇(F₂). Further, in the case z₃(x) in Equation (10), the minimumpositive integer satisfying Equation (6) is r=8, which indicates thatone cycle with a size of 32 exists on the Tanner graph H₃=E₈(F₃).

In addition, although the cycle structure of the QC-LDPC code is greatlyaffected by the parent matrix, the APM-LDPC code is less affected by theparent matrix when compared with the QC-LDPC code, which can bedemonstrated using Theorem 3.

Theorem 3

It is assumed that p number of overlaps exist between a 2l-sized blockcycle and a 2k-sized block cycle in an APM-LDPC code defined by an L×LAffine permutation matrix, and that function chains as given in thefollowing Equation (11) correspond to the block cycles, respectively:function chain 1: (ƒ₁,ƒ₂, . . . ,ƒ_(p),ƒ_(p+1),ƒ_(2l))function chain 2: (g₁,g₂, . . . ,g_(p),g_(p+1), . . . ,g_(2k))  (11)

In Equation (11), ƒ_(i)=g_(j) for i=1, 2, . . . , p. Further, it isassumed that function chains 1 and 2 have characteristic functions ofz₁(x)=a₁x+b₁ and z₂(x)=a₂x+b₂, respectively. Further, if it is assumedthat r is a minimum positive integer satisfying r(b₁−b₂+a₁b₂−a₂b₁)≡0 modL, the minimum cycle of the APM-LDPC code is 2r(2l+2k−p).

Irrespective of the size of the Affine permutation matrix, cycles causedby the overlaps between the block cycles may exist in the Tanner graphof the APM-LDPC code. Thus, if it is possible to remove as many blockcycle overlaps as possible from a parent matrix, many short-lengthcycles in a corresponding parity check matrix can be avoided. However,even if there is no overlap between block cycles, the upper limit of agirth is restricted by numerals related to two connected block cycles.

Theorem 4

FIG. 5 illustrates function chains of two different block cyclesconnected with each other by p number of blocks on the Tanner graphaccording to the present invention.

As illustrated in FIG. 5, it is assumed that two different block cycles,whose sizes are 2l and 2k, respectively, are connected with each otherby p number of blocks in an APM-LDPC code. Here, respective functionchains corresponding to the block cycles are given as represented by thefollowing Equation (12):function chain 1: (ƒ₁,ƒ₂, . . . ,ƒ₂l)function chain 2: (g₁,g₂, . . . ,g₂k)  (12)

Further, it is assumed that the connected blocks are (P^(h) ¹ , P^(h) ², . . . P^(h) ^(P) ), z_(i)(x)=a_(i)x+b_(i) is a characteristic functionof function chain i,

${\overset{p}{\underset{i = 1}{\odot}}{h_{i}^{{({- 1})}^{i}}(x)}} = {{{a_{3}x} + {b_{3}\mspace{14mu}{{and}\mspace{14mu}\overset{2k}{\underset{i = 1}{\odot}}{g_{i}^{{({- 1})}^{i + p}}(x)}}}} = {{a_{4}x} + {b_{4}.}}}$

Further, let r be a minimum positive integer satisfying the followingEquation (13):r(a ₃ b ₁(a ₄−1)−b ₄(a ₁−1)−b ₃(a ₁−1)(a ₄−1))≡0 mod L, when p≧1r(b ₁ −b ₂ +a ₁ b ₂ −a ₂ b ₁)≡0 mod L, when p=0  (13)

In this case, a girth of the corresponding APM-LDPC code is 4r(l+k+p).

Theorem 5

If it is assumed that for a prime number L, two different block cycles,whose sizes are 2l and 2k, respectively, are connected with each otherby p number of blocks in a parity check matrix of an APM-LDPC codedefined by an L×L Affine permutation matrix, a girth of the APM-LDPCcode is 4(l+k+p).

As described above, the present invention has an advantage in that it ispossible to transmit/receive a signal using an APM-LDPC code. Further,the present invention makes it possible to generate an APM-LDPC codecorresponding to an LDPC code which maximizes a girth while minimizingcomplexity, thereby providing an APM-LDPC code with superiorperformance.

While the invention has been shown and described with reference tocertain preferred embodiments thereof, it will be understood by thoseskilled in the art that various changes in form and details may be madetherein without departing from the spirit and scope of the invention asdefined by the appended claims.

1. A method for transmitting a signal in a communication system, themethod comprising: inputting an information vector; and generating a LowDensity Parity Check (LDPC) codeword by encoding the input informationvector in an Affine Permutation Matrix-Low Density Parity Check(APM-LDPC) encoding scheme, wherein the APM-LDPC encoding scheme is ascheme in which the information vector is encoded corresponding to aparity check matrix, and the parity check matrix includes (p×q) numberof blocks, to each of which an L×L-sized Affine permutation matrixcorresponds.
 2. The method as claimed in claim 1, further comprisingtransmitting the generated LDPC codeword.
 3. The method as claimed inclaim 1, wherein the Affine permutation matrix is expressed as:$\lbrack P^{f_{({a,b})}} \rbrack = \{ \begin{matrix}1 & {{{if}\mspace{14mu} f} = {f_{({a,b})}(i)}} \\0 & {otherwise}\end{matrix} $ where, P^(ƒ) ^((a,b)) denotes the Affinepermutation matrix, i and j denote a row index and a column index of theAffine permutation matrix, respectively, ƒ_((a,b)) denotes an Affinefunction on Z_(L)={0, 1, . . . , L−1}, Z_(L) is an integer ring ofmodulo L, and when Z*_(L)={iεZ_(L)|gcd(i,L)=1}, gcd is a greatest commondivisor, Z_(L)* is a conjugate of Z_(L), the Affine function ƒ_((a,b))is defined by ƒ_((a,b))(x)=ax +b, a εZ*_(L) and b εZ_(L).
 4. Anapparatus for transmitting a signal in a communication system, theapparatus comprising: an encoder for inputting therein an informationvector and generating a Low Density Parity Check (LDPC) codeword byencoding the input information vector in an Affine PermutationMatrix-Low Density Parity Check (APM-LDPC) encoding scheme, wherein theAPM-LDPC encoding scheme is a scheme in which the information vector isencoded corresponding to a parity check matrix, and the parity checkmatrix includes (p×q) number of blocks, to each of which an L×L-sizedAffine permutation matrix corresponds.
 5. The apparatus as claimed inclaim 4, further comprising a transmitter for transmitting the generatedLDPC codeword.
 6. The apparatus as claimed in claim 4, wherein theAffine permutation matrix is expressed as:$\lbrack P^{f_{({a,b})}} \rbrack = \{ \begin{matrix}1 & {{{if}\mspace{14mu} f} = {f_{({a,b})}(i)}} \\0 & {otherwise}\end{matrix} $ where, P^(ƒ) ^((a,b)) denotes the Affinepermutation matrix, i and j denote a row index and a column index of theAffine permutation matrix, respectively, ƒ_((a,b)) denotes an Affinefunction on Z_(L)={0, 1, . . . , L−1}, Z_(L) is an integer ring ofmodulo L, and when Z*_(L)={iεZ_(L)|gcd(i,L)=1}, gcd is a greatest commondivisor, Z_(L)* is a conjugate of Z_(L), the Affine function ƒ_((a,b))is defined by ƒ_((a,b))(x)=ax +b, a εZ*_(L) and b εZ_(L).
 7. A methodfor receiving a signal in a communication system, the method comprising:receiving a signal; and detecting an information vector by decoding thereceived signal in a decoding scheme corresponding to an AffinePermutation Matrix-Low Density Parity Check (APM-LDPC) encoding schemeapplied in a transmitter side, wherein the APM-LDPC encoding scheme is ascheme in which the information vector is encoded corresponding to aparity check matrix, and the parity check matrix includes (p×q) numberof blocks, to each of which an L×L-sized Affine permutation matrixcorresponds.
 8. The method as claimed in claim 7, wherein the Affinepermutation matrix is expressed as:$\lbrack P^{f_{({a,b})}} \rbrack = \{ \begin{matrix}1 & {{{if}\mspace{14mu} j} = {f_{({a,b})}(i)}} \\0 & {otherwise}\end{matrix} $ where, P^(ƒ) ^((a,b)) denotes the Affinepermutation matrix, i and j denote a row index and a column index of theAffine permutation matrix, respectively, ƒ_((a,b)) denotes an Affinefunction on Z_(L)={0, 1, . . . , L−1}, Z_(L) is an integer ring ofmodulo L, and when Z*_(L)={iεZ_(L)|gcd(i,L)=1}, gcd is a greatest commondivisor, Z_(L)* is a conjugate of Z_(L), the Affine function ƒ_((a,b))is defined by ƒ_((a,b))(x)=ax +b, a εZ*_(L) and b εZ_(L).
 9. Anapparatus for receiving a signal in a communication system, theapparatus comprising: a receiver unit for receiving a signal; and adecoder for detecting an information vector by decoding the receivedsignal in a decoding scheme corresponding to an Affine PermutationMatrix-Low Density Parity Check (APM-LDPC) encoding scheme applied in atransmitter side, wherein the APM-LDPC encoding scheme is a scheme inwhich the information vector is encoded corresponding to a parity checkmatrix, and the parity check matrix includes (p×q) number of blocks, toeach of which an L×L-sized Affine permutation matrix corresponds. 10.The apparatus as claimed in claim 9, wherein the Affine permutationmatrix is expressed as:$\lbrack P^{f_{({a,b})}} \rbrack = \{ \begin{matrix}1 & {{{if}\mspace{14mu} f} = {f_{({a,b})}(i)}} \\0 & {otherwise}\end{matrix} $ where, P^(ƒ) ^((a,b)) denotes the Affinepermutation matrix, i and j denote a row index and a column index of theAffine permutation matrix, respectively, ƒ_((a,b)) denotes an Affinefunction on Z_(L)={0, 1, . . ., L−1}, Z_(L) is an integer ring of moduloL, and when Z*_(L)={iεZ_(L)|gcd(i,L)=1}, gcd is a greatest commondivisor, Z_(L)* is a conjugate of Z_(L), the Affine function ƒ_((a,b))is defined by ƒ_((a,b))(x)=ax +b, a εZ*_(L) and b εZ_(L).